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Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 54 and estimated standard deviation σ = 43. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
(a) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.The probability distribution of x is approximately normal with μx = 54 and σx = 30.41.
b)What is the probability that x < 40? (Round your answer to four decimal places.)
c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
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